Auxiliary Field Sigma Models and Yang-Baxter Deformations

We combine the Yang-Baxter deformation with higher-spin auxiliary field deformations to construct a multi-parameter family of integrable deformations of the principal chiral model on a Lie group $G$ with semi-simple Lie algebra $\mathfrak{g}$. Our construction produces one integrable deformation for each pair $(\mathcal{R}, E)$, where $\mathcal{R}$ is an antisymmetric bilinear operator on $\mathfrak{g}$ obeying the modified classical Yang-Baxter equation and $E$ is a function of several variables. We show that every model in this family is (weakly) classically integrable by exhibiting a Lax representation for its equations of motion.